Guidance

This Concept focuses on the area of a triangle. Previously we learned that
triangle
is a three sided figure made up of line segments with three sides and three angles.
Area
is the amount of space inside a two-dimensional figure.
We can find the area of a triangle just like we found the area of a parallelogram.
The really interesting thing is that the area of a triangle is related to the area of a parallelogram.
Take a look at this figure.

Notice that the parallelogram has been divided into two triangles.

We know that the formula for finding the area of a parallelogram requires us to multiply the base times the height. Well, if a triangle is one-half of a parallelogram, can you figure out the formula for finding the area of a triangle?

Here it is.

It certainly does. With this formula, the area of a triangle will be snap to figure out!

Take a minute to write this formula down in your notebook.

Now that you can identify formula for finding the area of a triangle, let’s look at using it in problem solving.

Find the area of the triangle below.

We can see that the base is 11 centimeters and the height is 16 centimeters. We simply put these numbers into the appropriate places in the formula.

Remember that we always measure area in square units because we are combining two dimensions. The area of this triangle is 88 square centimeters. Let’s try another.

What is the area of the triangle below?

Notice that the height is shown by the dashed line. It is perpendicular to the base. We put it and the base into the formula and solve.

The area of this triangle is 42.5 sq. cm. Now it’s time for you to try a few on your own.

Find the area of each triangle.

Example A

Base = 12 in, height = 6 inches

Solution:

Example B

Base = 9 inches, height = 4 inches

Solution:

Example C

Base = 11 inches, height = 7 inches

Solution:

Here is the original problem once again.

Miguel saw gardening designs on Center Street. As he was walking, he noticed a series of triangles that line the median. The triangles are overlapping.

Let’s say that that the first triangle has a base of 6 feet and a height of 5 feet.

What is the area of the triangle?

To figure this out, we can start with the formula for finding the area of a triangle.

Let’s say that there are eight triangles in this strip of median. We can take the area of one of the triangles and multiply it by 8.

15(8) = 120 square feet

This is the area of the median. We were able to use the area of each triangle to find the total area of the median.